Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 246808, 13 pages
doi:10.1155/2010/246808
Research Article

Strong Convergence Theorem for a New General System of Variational Inequalities in Banach Spaces

S. Imnang1,2 and S. Suantai2,3

1Department of Mathematics, Faculty of Science, Thaksin University, Phatthalung Campus, Phatthalung 93110, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Received 26 July 2010; Revised 7 December 2010; Accepted 30 December 2010

Academic Editor: S. Reich

Copyright © 2010 S. Imnang and S. Suantai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce a new system of general variational inequalities in Banach spaces. The equivalence between this system of variational inequalities and fixed point problems concerning the nonexpansive mapping is established. By using this equivalent formulation, we introduce an iterative scheme for finding a solution of the system of variational inequalities in Banach spaces. Our main result extends a recent result acheived by Yao, Noor, Noor, Liou, and Yaqoob.